Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-8y &= 9 \\ -8x-9y &= 3\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-8x = 9y+3$ Divide both sides by $-8$ to isolate $x$ $x = {-\dfrac{9}{8}y - \dfrac{3}{8}}$ Substitute this expression for $x$ in the first equation. $-5({-\dfrac{9}{8}y - \dfrac{3}{8}}) - 8y = 9$ $\dfrac{45}{8}y + \dfrac{15}{8} - 8y = 9$ Simplify by combining terms, then solve for $y$ $-\dfrac{19}{8}y + \dfrac{15}{8} = 9$ $-\dfrac{19}{8}y = \dfrac{57}{8}$ $y = -3$ Substitute $-3$ for $y$ in the top equation. $-5x-8( -3) = 9$ $-5x+24 = 9$ $-5x = -15$ $x = 3$ The solution is $\enspace x = 3, \enspace y = -3$.